.4832x^2+.37166x-.0096=0

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Solution for .4832x^2+.37166x-.0096=0 equation:


Simplifying
0.4832x2 + 0.37166x + -0.0096 = 0

Reorder the terms:
-0.0096 + 0.37166x + 0.4832x2 = 0

Solving
-0.0096 + 0.37166x + 0.4832x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.4832 the coefficient of the squared term: 

Divide each side by '0.4832'.
-0.01986754967 + 0.7691639073x + x2 = 0

Move the constant term to the right:

Add '0.01986754967' to each side of the equation.
-0.01986754967 + 0.7691639073x + 0.01986754967 + x2 = 0 + 0.01986754967

Reorder the terms:
-0.01986754967 + 0.01986754967 + 0.7691639073x + x2 = 0 + 0.01986754967

Combine like terms: -0.01986754967 + 0.01986754967 = 0.00000000000
0.00000000000 + 0.7691639073x + x2 = 0 + 0.01986754967
0.7691639073x + x2 = 0 + 0.01986754967

Combine like terms: 0 + 0.01986754967 = 0.01986754967
0.7691639073x + x2 = 0.01986754967

The x term is 0.7691639073x.  Take half its coefficient (0.3845819537).
Square it (0.1479032791) and add it to both sides.

Add '0.1479032791' to each side of the equation.
0.7691639073x + 0.1479032791 + x2 = 0.01986754967 + 0.1479032791

Reorder the terms:
0.1479032791 + 0.7691639073x + x2 = 0.01986754967 + 0.1479032791

Combine like terms: 0.01986754967 + 0.1479032791 = 0.16777082877
0.1479032791 + 0.7691639073x + x2 = 0.16777082877

Factor a perfect square on the left side:
(x + 0.3845819537)(x + 0.3845819537) = 0.16777082877

Calculate the square root of the right side: 0.409598375

Break this problem into two subproblems by setting 
(x + 0.3845819537) equal to 0.409598375 and -0.409598375.

Subproblem 1

x + 0.3845819537 = 0.409598375 Simplifying x + 0.3845819537 = 0.409598375 Reorder the terms: 0.3845819537 + x = 0.409598375 Solving 0.3845819537 + x = 0.409598375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3845819537' to each side of the equation. 0.3845819537 + -0.3845819537 + x = 0.409598375 + -0.3845819537 Combine like terms: 0.3845819537 + -0.3845819537 = 0.0000000000 0.0000000000 + x = 0.409598375 + -0.3845819537 x = 0.409598375 + -0.3845819537 Combine like terms: 0.409598375 + -0.3845819537 = 0.0250164213 x = 0.0250164213 Simplifying x = 0.0250164213

Subproblem 2

x + 0.3845819537 = -0.409598375 Simplifying x + 0.3845819537 = -0.409598375 Reorder the terms: 0.3845819537 + x = -0.409598375 Solving 0.3845819537 + x = -0.409598375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3845819537' to each side of the equation. 0.3845819537 + -0.3845819537 + x = -0.409598375 + -0.3845819537 Combine like terms: 0.3845819537 + -0.3845819537 = 0.0000000000 0.0000000000 + x = -0.409598375 + -0.3845819537 x = -0.409598375 + -0.3845819537 Combine like terms: -0.409598375 + -0.3845819537 = -0.7941803287 x = -0.7941803287 Simplifying x = -0.7941803287

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.0250164213, -0.7941803287}

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